Thin strips of elastic stretchable plastic material have become widely used for wrapping goods or boxes of goods to be stored or shipped. For example, it is common practice to stack a plurality of boxes on a pallet for shipping and to secure the boxes together, and with respect to the pallet, by wrapping them with a film or strip of resilient plastic material or, in other words, a stretch-wrap. Such stretch-wrapped materials are quite thin and are subject to rupturing or tearing at the edges, particularly in situations where the goods being wrapped have relatively sharp corners or uneven surfaces. Heretofore, it has been suggested to reinforce the edges of such stretch-wrapped materials by gathering or bunching the edges together so as to provide a so-called hem. While such hemming is effective for reinforcing the edges, the bunching may be uneven in appearance and effectiveness and provides ribs or ridges in the ultimate package, which may be objectionable.